Block #682,332

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/18/2014, 4:58:57 AM · Difficulty 10.9608 · 6,125,692 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

bb8bf8468a09d5f6261b7337a1546f62079f71fe8276fb26c4576d62bba86cd2

View on Chainz ↗

Height

#682,332

Difficulty

10.960789

Transactions

Size

1.52 KB

Version

Bits

0af5f64a

Nonce

1,935,872,458

Timestamp

8/18/2014, 4:58:57 AM

Confirmations

6,125,692

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5ed56f91d62d50ae61092f00555518a3dc1244160e66e93367be45768371c7e9

Transactions (5)

Coinbase2683574c8fc585…cf2d0f5bf7c3ab

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

27710d84ebfc65…da96eaa5c7dbb5

1 in → 2 out3069.3047 XPM226 B

AeHpxk2n…Vs2pa37j ARMmjyvz…4PLUTMJK

a35f5c06505139…57e92301468888

1 in → 2 out7.2657 XPM225 B

AS9ZCvju…bu3NEFwZ Ac9hjDKN…aXYG9E3G

93c488247d60ae…0a90e2108b216b

1 in → 2 out1.2330 XPM226 B

AbQx2wDj…kAQmsZ7h Abs1CTRR…uk6ieBYF

a42e0da69bfd56…59938a40917956

4 in → 2 out5.1409 XPM669 B

ATUJFkEF…j71DTZhm AZbaekWS…Z69Rszk8

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.678 × 10⁹⁶(97-digit number)

86784825638164023659…59356619040858658079

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

8.678 × 10⁹⁶(97-digit number)

86784825638164023659…59356619040858658079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.678 × 10⁹⁶(97-digit number)

86784825638164023659…59356619040858658081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.735 × 10⁹⁷(98-digit number)

17356965127632804731…18713238081717316159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.735 × 10⁹⁷(98-digit number)

17356965127632804731…18713238081717316161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.471 × 10⁹⁷(98-digit number)

34713930255265609463…37426476163434632319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.471 × 10⁹⁷(98-digit number)

34713930255265609463…37426476163434632321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

6.942 × 10⁹⁷(98-digit number)

69427860510531218927…74852952326869264639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.942 × 10⁹⁷(98-digit number)

69427860510531218927…74852952326869264641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.388 × 10⁹⁸(99-digit number)

13885572102106243785…49705904653738529279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.388 × 10⁹⁸(99-digit number)

13885572102106243785…49705904653738529281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.777 × 10⁹⁸(99-digit number)

27771144204212487570…99411809307477058559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #682,332

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